Miracles and Leibniz’s Principle of Least Action

by Max Andrews

The principle of least action states that God always chooses the most minimal means by which to produce the world. For example, if God had the choice to intervene in the world three times or five times but he would still receive identical glory for either number of interventions then God would always choose the minimal means (three interventions). I believe this principle bears truth, if anything it is quite attractive. Now how does this compare with God’s interventions via miracles? Let’s define a miracle as: A divine intervention into, or an interruption of, the regular course of the world that produces a purposeful but unusual event that would not have occurred otherwise. Miracles are not violations of laws of causality.

Are miracles thus dependent on strong actualizations or will weak actualizations be sufficient (God weakly actualizes S iff there is an S* such that God strongly actualizes [direct causation] S* and S* → S, where → is “counterfactual implication” [Let S be a state of affairs])? It seems that strong actualization is the most obvious or most appealing means by which God intervenes (miracles), but perhaps weakly actualized miracles is more in sync with the principle of least action. Perhaps at the initial conditions of the universe God constructed the world in such a way that the miracle would happen naturally given the states of affairs at the time of the miracle (including physical states and counterfactuals of human freedom). This could have been the case that a natural quantum perturbation/anomalous event occurs at the time of the resurrection, thus, it is weakly actualized. (Now this includes all historical/physical events in time preceding the resurrection but this perturbation is not strongly/directly caused. In other words, God does not introduce a new cause into the already existing cause and effect system). It would still be a miracle given the religio-historical context which surround the miracle, which God anticipated. These weakly actualized miracles that occur naturally are not mere natural events given the background information. If weakly actualized miracles are a priori defined out of existence by the definition given, then if weakly actualized miracles are plausible, perhaps we need a new working definition. This begs the question, which, for God, is the least course of action: weakly actualized miracles or strongly actualized miracles?

3 Comments
to “Miracles and Leibniz’s Principle of Least Action”

I’m having a difficult time seeing how God’s weakly actualizing a state of affairs can be a legit miracle. Does God ever, in your book, strongly actualize a state of affairs in the world? If so, isn’t *that* what we mean by ‘miracle’? If not, and miracles really are just weakly actualized, but naturally occurring states of affairs, how, then, can they be considered miraculous? Is it simply because we didn’t see them coming? Is it simply because our calculus with respect to the laws of nature was off for some reason or another? If so, then these aren’t miracles; they’re just unexpected natural phenomena that, had we known better, we could have seen coming all along. They followed deterministically from the conjunction of the past and the laws of nature. What’s so miraculous about that?

What’s more, your thesis comes really close to sounding like any weakly actualized state of affairs whatever might be considered a miracle. But that’s the vast majority of actualized states of affairs. I supposed you could respond by saying ‘No, no. The probability has to be really low.’ But, then I’d submit to you that the probability is only ‘low’ because we lacked the requisite knowledge (and the perfected calculus) to see the state of affairs’s coming. There isn’t anything improbable *at all* about any naturally occurring state of affairs. They follow necessarily from the conjunction of the past and the laws of nature.

I don’t think you want to give up the ghost (with respect to the miraculous) quite so easily.

I do believe that God strongly actualizes states of affairs in the world but I don’t believe these actualizations are miracles. God can directly cause me to be convicted about something or introduce a thought into my mind by direct causation, but I don’t think those are miracles. I think the problem upfront is the problem of defining a miracle contingent on it being weakly/strongly actualized because the definition I give could potentially define it out of existence. A weakly actualized miracle is different from a mere natural event because it was predetermined to occur, as if God programmed the universe to function at t1 in such a way that the event [miracle] occurs at time t2 without an introduction of a new cause at t2 but that cause was really introduced at t1 but the effect is not present until t2 (if this makes any sense at all lol). I think the religio-historical background is important as well so it can be distinguished from a mere [immediately] purposeless event (such as Jesus make claims and the resurrection validating such claims). These weakly actualized miracles may still fit in the definition given because had God not set up such initial conditions by implementing the necessary cause/effect relationships at the beginning it may be the case that the event [miracle] not occur (but then again we may have a completely different world on our hands at that point). I guess, in essence, if our knowledge of such initial conditions were so well known then it could be the case that we could attain such knowledge sufficient enough to predict such events (though highly unlikely given the probability calculous of QM already, but in theory, yes). That may be less attractive, to me it is at least, but I don’t have a sufficient reason for why I don’t like that, as you’ve pointed out about the calculus. I don’t think that would rob God of any glory or take miracles out of existence because I don’t think we will ever attain such knowledge (though it’s possible). I don’t want to commit to Newton’s machine universe because given free agency, we can introduce new cause and effects into the already existing system, where the causes would still resume, but I think agent involvement eliminates a physical determinism with respects to the necessity of certain events happening on a small open system such as the earth. Now with inflation and macro level laws, no hope for our interference there lol.

This whole thing began with an argument for deism when reading Leibniz. I didn’t like my argument because I found myself persuasive, but after I sat on it for a couple days I realized that weak actualization may actually not fit to the principle of least action. The principle may be entirely appropriate and fitting to strongly actualized miracles. I haven’t ruled either out, I actually prefer strongly actualized miracles because it seems to be more compatible with the principle given so may prior states of affairs between the cause and it’s effect. I wonder if I made any sense at all here but thanks for the thoughts and response lol

I googled “miracles and the principle of least action” hoping to learn whether anyone has considered the role the variational principle plays in physical laws. Briefly, Noether’s theorem correlates conservation laws (of energy, momentum, and charge for example) with symmetries of the Lagrangian and various field theories, so long as the action is minimized (or extremized).
Whenever I hear discussions of miracles and violating the laws of nature I rarely hear any mention of whether the action (the integral of the Lagrangian density) would remain minimized during a miracle. There’s no law (as far as I am aware) requiring that the action be minimized. It’s just a very successful principle for deriving physical laws. And if the action is not minimized in a region of space-time then the typical laws would not obtain in that region. From this perspective, the laws of physics are not sacred so much as they describe what happens when the action is left minimized. When the action is not minimized, there seems to be flexibility for divine intervention. Anyway, I’m just thinking out loud here, not a very well developed approach yet.